What is the value of the y-coordinate of the y-intercept of the function shown below? F(x)=-3x^2+5x-4

Answers

Answer 1

Answer:

The y-coordinate of the y-intercept is [tex]-4[/tex]

Step-by-step explanation:

we know that

The y-intercept is the value of y when the value of x is equal to zero

so

In this problem we have

[tex]F(x)=-3x^2+5x-4[/tex]

Find the y-intercept

For [tex]x=0[/tex]

[tex]F(0)=-3(0)^2+5(0)-4=-4[/tex]

The y-intercept is the point [tex](0,-4)[/tex]

therefore

The y-coordinate of the y-intercept is [tex]-4[/tex]

Answer 2

Answer:

The value would be -4.

Step-by-step explanation:


Related Questions

Dam has been asked to post a parcel for a family member. He has been told that the parcel weighs 12 lbs 8 oz.

Answers

Answer:

The weight of the parcel is approximately 6 kilograms.

Step-by-step explanation:

The weight of the parcel is  12 lbs and 8 oz.

1 lb = 16 oz

So,  8 oz =  lb.

That means,  12 lbs and 8 oz = (12 + 0.5) lbs = 12.5 lbs

Now, 1 lb = 454 g

So,  12.5 lbs = (12.5 × 454) g = 5675 g

As,  1 kilogram = 1000 g

That means, 1 g = 0.001 kilogram

So,  5675 g  kilograms. (Rounded to the nearest whole kilogram)

Thus, the weight of the parcel is approximately 6 kilograms.

Under which operations are polynomials closed? Addition, subtraction, multiplication, and division addition and subtraction only addition, subtraction, and multiplication only addition and multiplication only

Answers

Answer:

addition, subtraction, and multiplication only

Step-by-step explanation:

There are a couple of reasons why polynomials are not closed under division:

1. the set of polynomials includes zero, and division by zero is undefined.

2. division by a polynomial can give rise to terms that are not non-negative powers of the variable, 1/x, for example. These terms are not included in the set of polynomials.

Answer:

Addition, Subtraction, and Multiplication

Step-by-step explanation:

The length of the edges of the triangle are (3x-4) feet, (x2-1)feet, and (2x-15) feet. What's is the perimeter of the triangle if x=4

Answers

Answer:

40 feet

Step-by-step explanation:

The perimeter of a triangle is the distance around the triangle. It can be found by adding all the sides together. First, find the amount each side is by substituting x = 4 and simplifying.

3x - 4 = 3(4) - 4 = 12 - 4 = 8

x² -1 = (4)² - 1 = 16 - 1 = 15

2x² - 15 = 2(4)² - 15 = 32 - 15 = 17

Add the sides together, 8 + 15 + 17 = 40 feet

HELP ASAP 23 points
A $250 table is on sale at 15% off. What are the discount and sale price of the table?

Answers

The discount is $37.50 and the sale price of the table is $212.50.

We have to calculate the discount and sale price

Discount

Discount amount =

Original price * Discount percentage

Discount amount = $250 * 15%

= $250 * 0.15

= $37.50

Sale price

Sale price = Original price - Discount amount

Sale price = $250 - $37.50

= $212.50

Find the value of a cylinder with a diameter of 8 inches and a height that is three times the radius

Answers

Answer:

nevermind

Step-by-step explanation:

Help ASAP Please!!!!

Which function includes a translation of 3 units to the left?

A. f(x)= (x+1)^2-3

B. f(x)= (x+3)^2+1

C. f(x)= 3x^2+1

D. f(x)= (x-3)^2+1

Answers

Answer:

It's B.   f(x) = (x + 3(^2 + 1.

Step-by-step explanation:

f(x) ---- > f(x + 3)   is a translation of 3 units to the left.

Final answer:

The correct function that includes a 3 unit leftward translation is f(x) = [tex](x-3)^2+1.[/tex]

Explanation:

The correct function that includes a translation of 3 units to the left is option D, f(x) = [tex](x-3)^2+1.[/tex]

When we translate a function to the left by a certain number of units, we subtract that number from the x-values. In this case, subtracting 3 units from x would result in a translation to the left. The function f(x) = [tex](x-3)^2+1.[/tex] represents this translation. The x-3 part shifts the graph horizontally to the left by 3 units.

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A bag contains 4 green marbles, 6 red marbles, 14 orange marbles, 5 brown msrbles, and 8 blue marbles. You choose a marble, replace it, and choose again. What is P(red, then blue)?

Answers

BRAINLY IF YOU CAN SEE THIS PLZ MAKE IT SO THAT YOU CAN ONLY GET POINTS BY PEOPLE SAYING THANKS TO YOUR ANSWER. IF YOU DONT, PEOPLE DO STUFF LIKE WHAT THE OTHER PERSON DID.

[tex]\frac{48}{1369}[/tex]

Step-by-step explanation:

A bag contains 4 green marbles, 6 red marbles, 14 orange marbles, 5 brown marbles, and 8 blue marbles. You choose a marble, replace it, and choose again. Total marbles = 37 marbles

Probability (choosing red) = number of red marbles / total marbles

= 6/37

Red is replaces so total marbles again becomes 37

P( choosing blue)= 8/37

P(red, then blue)= [tex]\frac{6}{37} * \frac{8}{37} = \frac{48}{1369}[/tex]

The corresponding polynomial function is f(x) = x2 + 5x - 1 f(x) = x2 + 4x - 5 f(x) = x2 + 5x - 5 f(x) = x2 - 4x - 5

Answers

Answer:

f(x)=x^2+4x-5

Step-by-step explanation:

Final answer:

Quadratic functions are second-order polynomials. To solve a quadratic equation, set the function equal to zero, and use the quadratic formula. The corresponding polynomial function in this case is f(x) = x² + 5x - 1.

Explanation:The Solution of Quadratic Equations

Quadratic functions are second-order polynomials. They are of the form f(x) = ax² + bx + c, where a, b, and c are constants. To solve a quadratic equation, set the function equal to zero, and use the quadratic formula: x = (-b ± √(b²-4ac))/(2a). The discriminant, b²-4ac, determines the number and nature of the solutions. If the discriminant is positive, there are two real solutions. If it is zero, there is one real solution (a perfect square). If it is negative, there are no real solutions, but there are two complex solutions.

In this case, the corresponding polynomial function is f(x) = x² + 5x - 1.

Question 1(Multiple Choice Worth 2 points) Find the derivative of f(x) = 7 divided by x at x = 1.
-7
-1
1
7
Question 2(Multiple Choice Worth 2 points) Find the derivative of f(x) = 4x + 7 at x = 5.
4
1
5
7
Question 3(Multiple Choice Worth 2 points) Find the derivative of f(x) = 12x2 + 8x at x = 9.
256
-243
288
224
Question 4(Multiple Choice Worth 2 points) Find the derivative of f(x) = negative 11 divided by x at x = 9.
11/9
81/11
9/11
11/81
Question 5 (Essay Worth 2 points) The position of an object at time t is given by s(t) = 1 - 10t. Find the instantaneous velocity at t = 10 by finding the derivative.

Answers

1. Answer: a. -7

Step-by-step explanation:

[tex]f(x)=\dfrac{7}{x}\implies f(x)=7x^{-1}\\\\f'(x)=-1\cdot 7x^{-1-1}\\.\qquad =-7x^{-2}\\\\.\qquad =-\dfrac{7}{x^2}\\\\f'(1)=-\dfrac{7}{1^2}\\\\.\qquad =\large\boxed{-7}[/tex]

2. Answer: a. 4

Step-by-step explanation:

[tex]f(x)=4x+7\\f'(x)=1\cdot4x^{1-1}+0\cdot7\\.\qquad=4\\\\f'(5)=\large\boxed{4}[/tex]

3. Answer: d. 224

Step-by-step explanation:

[tex]f(x)=12x^2+8x\\f'(x)=2\cdot12x^{2-1}+1\cdot8x^{1-1}\\.\qquad=24x+8\\\\f'(9)=24(9)+8\\.\qquad=216+8\\.\qquad=\large\boxed{224}[/tex]

4. Answer: d. 11/81

Step-by-step explanation:

[tex]f(x)=\dfrac{-11}{x}\implies f(x)=-11x^{-1}\\\\f'(x)=-1\cdot -11x^{-1-1}\\\\.\qquad=11x^{-2}\\\\.\qquad=\dfrac{11}{x^2}\\\\f'(9)=\dfrac{11}{9^2}\\\\.\qquad=\large\boxed{\dfrac{11}{81}}[/tex]

5. Answer: -10

Step-by-step explanation:

s(t) = 1 - 10t

v = s'(t) = -10

     s'(10) = -10

(Q6) What is the domain of the function f(x)= e^x/e^x+c if c is a constant greater than 0?

Answers

[tex]Domain: x\in\mathbb{R}[/tex]

Simplify the irrational number 128; then estimate it to two decimal places.

Answers

Final answer:

The square root of 128, which is an irrational number, is approximately 11.304. Rounded to two decimal places, it becomes 11.30.

Explanation:

The process of simplifying the irrational number 128 involves finding a square root since irrational numbers are those that cannot be expressed as a simple fraction, such as roots that are not even. The square root of 128 is not a whole number, therefore it's an irrational number. Using a calculator, the square root of 128 is approximately 11.304. So to obtain the square root of 128 to two decimal places, you round 11.304 to 11.30.

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What is the area of a triangle with a=25 b=13 and c=17? (picture provided)

Answers

For this case we must find the area of a scalene triangle (different sides) by means of Heron's formula:

[tex]S = \sqrt {p (p-a) (p-b) (p-c)}[/tex]

Where:

S: It's the area

p: It is the semiperimeter

a, b, c: They are the sides:

[tex]p = \frac {a + b + c} {2}\\p = \frac {25 + 13 + 17} {2}\\p = 27.5 \ units[/tex]

So:

[tex]S = \sqrt {27.5 (27.5-25) (27.5-13) (27.5-17)}\\S = \sqrt {10467.1875}\\S = 102.309 \ units ^ 2[/tex]

ANswer:

Option D

How are slopes and y-intercepts related to the number of solutions of a system of linear equations

Answers

Explanation:

For a system of 2 equations in 2 unknowns, there are 3 cases:

slopes are different — one solutionslopes are the same and y-intercepts are different — no solutionsslopes and y-intercepts are the same — infinitely many solutions

When slopes are different, the two lines intersect at one point, the solution.

When slopes are the same, the lines may be either parallel (different y-intercepts) or the same (same y-intercepts). If the lines are parallel, there are no points of intersection, hence no solutions. If the lines are the same line, they intersect at all points, so there are infinitely many solutions.

Explain why f(x) is continuous at x=3

Answers

Answer:

f is not  defined at x = 3 ⇒ answer (b)

Step-by-step explanation:

∵ f(x) = x² - x - 6/x² - 9 is a rational function

∴ It will be undefined at the values of x of the denominator

∵ The denominator is x² - 9

∵ x² - 9 = 0 ⇒ x² = 9 ⇒ x = ±√9

∴ x = ± 3

∴ f(x) can not be defined at x = 3

∴ The f(x) can not be continuous at x = 3

∴ The answer is (b)

Answer:

b. f is not defined at x=3

Step-by-step explanation:

The given function is

[tex]f(x)=\frac{x^2-x-6}{x^2-9}[/tex]

One of the conditions for continuity is that; the function must be defined at [tex]x=a[/tex]

If we plug in [tex]x=3[/tex], we obtain;

[tex]f(x)=\frac{3^2-3-6}{3^2-9}[/tex]

[tex]f(x)=\frac{9-3-6}{9-9}[/tex]

[tex]f(x)=\frac{0}{0}[/tex]

Since the function is not defined at x=3, it is not also continuous at x=3

The correct choice is B

A cooler is filled with different juices. There are 24 bottles of juice: 6 orange juice, 4 apple juice, 2 cranberry juice, and 12 grape juice. Julie is choosing juice at random for herself and a friend. What is the probability that she chooses 1 orange juice and then 1 apple juice?

Answers

Answer:

for the orange juice it's 6/24

for the apple juice it's 4/24

Step-by-step explanation:

since there are 24 juices you need to put the denominator as 24 at all time no matter the juice choice and then you find how many there are of that specific juice and put it as the top number because that is the probability of you getting that specific juice.

Pleased give me the brainliest answer. :)

Use the substitution method to solve the system of equations. choose the correct ordered pair.
3x- y=3
Y=2x +2

A. (2,6)
B. (5,12)
C. (4,10)
D.(3,8)

Answers

Answer: Choice B. (5, 12)

=============================================

Explanation:

Start with the first equation. We'll plug in y = 2x+2

3x - y = 3

3x - ( y ) = 3

3x - ( 2x+2 ) = 3 ..... replace y with 2x+2

3x - 2x - 2 = 3 ..... distribute the negative through to all terms inside

x-2 = 3  ............ combine like terms

x-2+2 = 3+2 .... add 2 to both sides

x = 5

Use this x value to find the value of y. The easiest equation to use is the one in which y is already isolated for us

y = 2x+2

y = 2*5+2 ..... replace x with 5

y = 10+2

y = 12

Though we can use the other equation as well

3x-y = 3

3*5-y = 3 .... replace x with 5

15 - y = 3

15-y-15 = 3-15 ..... subtract 15 from both sides

-y = -12

y = 12 ..... multiply both sides by -1, or change the signs of both sides

We get the same result for y.

The solution is (x,y) = (5,12) meaning that the graphs of the two original equations cross at this point.

It’s 5 & 12. Just substitute them in and boom!

What facts are true for the graph of the function listed below? Please check all that apply.

F(x)=2 x 5^x

Answers

Answer:

E, B, A,

Step-by-step explanation:

C is wrong because it isn't decreasing

D is wrong because if X=0 the 5 to the power of zero would be 1 and 2*1= 2 meaning y goes lower than 5

F is wrong because  if X=0 the 5 to the power of zero would be 1 and 2*1= 2 meaning the y intercept is 2 not 5

Answer:

[tex]\Large \boxed{\mathrm{A , \ B, \ and \ E}}[/tex]

Step-by-step explanation:

[tex]F(x)=2 \cdot 5^x[/tex]

There are no restrictions on x. The domain is all real numbers.

To find the y-intercept, we set the x value to 0. The y-intercept of the function is (0, 2).

The function is increasing, because as the value of the input increases, the value of the output increases as well.

Please answer this question only if you know the answer!!! :)

Answers

A full circle is 360 degrees.

The circle is separated into 8 parts, so each arc is 1/8 of a circle, which equals: 360/8 = 45 degrees.

There are 2 45 degree arcs between B and C, so the arc from B to C = 45 x 2 = 90 degrees.

The answer is B.

Add both the numerators and the denominators when adding fractions and mixed numbers. True False

Answers

Answer:

false

Step-by-step explanation:

Add both the numerators and the denominators when adding fractions and mixed numbers - this statement is false.

How to add numerators and  denominators  adding fractions and mixed numbers:

To add fractions with  denominators, first find a common denominator. The least common denominator is easiest to use. The least common multiple can be used as the least common denominator. Adding mixed numbers involves adding the fractional parts, adding the whole numbers, and then recombining them as a mixed number.

1. Add the whole numbers together.

2. Find the lowest common denominator of both fractions.

3. Convert the fractions to have the LCD as their denominator.

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Please answer this question, will give brainliest!

Answers

There are 360° in a circle and this circle is divided into 8 equal parts. 360/8 = 45 which means that each angle is 45°. The central angle subtended by minor arc BC is 2 portions of the circle, or 45 * 2 which is 90°. The answer is B.

Answer:

The answer should be B, 90.

Step-by-step explanation:

The circle is broken up into 8, 45 degree angles. the subtended of arc BC should be 90, tell me if i'm wrong.

Mark brainliest plz thanks!

Renee writes a number that is the same distance from 0 as 7 on a number line but in the other direction. What number did Renee write?

Answers

ANSWER

-7

EXPLANATION

The only numbers that have a distance of 7 from zero on the real number line are -7 and 7.

-7 is to the left of zero while 7 is to the right of zero.

But this two numbers are all 7 units from zero.

In other words, the absolute values of this numbers is 7.

[tex] |x| = 7[/tex]

[tex]x = - 7 \: or \: 7[/tex]

Hence the number Renee wrote is -7

Final answer:

The number that is the same distance from 0 as 7 on a number line, but in the opposite direction, is -7. This is because on a number line, +7 is 7 units to the right of 0 and -7 is 7 units to the left of 0.

Explanation:

In the field of Mathematics, the concept of a number line is a tool to understand the placement of numbers and their relative distance to one another. If Renee writes a number that is the same distance from 0 as 7 on a number line, but in the opposite direction, the number she writes would be -7.

This is because on a number line, the positive direction (to the right) signifies adding and the negative direction (to the left) signifies subtracting from zero. So the number -7 is 7 units distance to the left of 0. Similarly, the number 7 is 7 units distance to the right of 0. Hence, both numbers -7 and +7 are equidistant from 0, but lie in opposite directions on the number line.

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A cylinder with radius 3 feet and height 5 feet is shown. Enter the volume of the cylinder in cubic feet. Round your answer to the nearest hundredth.

Answers

volume of the cylinder= pi r^2 h

=22/7*3*3*5=141.428

nearest hundredth =141.420

volume of the given cylinder= 141.42 cubic feet

Answer:

The volume of the cylinder is 141.43 ft³.

Step-by-step explanation:

Since, the volume of a cylinder is,

[tex]V=\pi (r)^2 h[/tex]

Where, r is the radius of the cylinder,

And, h is the height of the cylinder,

Here, r = 3 feet,

h = 5 feet,

Hence, the volume of the given cylinder is,

[tex]V=\pi (3)^2 (5)[/tex]

[tex]=\frac{22}{7}\times 9\times 5[/tex]     (  [tex]\pi =\frac{22}{7}[/tex] )

[tex]=\frac{990}{7}[/tex]

[tex]=141.428571429\text{ cube feet}=141.43\text{ cube feet}[/tex]

A random experiment has three steps with three outcomes possible for the first step, two outcomes possible for the second step, and four outcomes possible for the third step. how many experimental outcomes exist for the entire experiment?

Answers

Answer: 6 outcomes

Step-by-step explanation: Since the first outcome is 2 and the second is 4 2 times 3 is ix since it is multiplying by 2 (2,4,6,8)

Final answer:

To find the total number of experimental outcomes for the entire experiment, multiply the number of outcomes for each step together, resulting in 24 total experimental outcomes.

Explanation:

The total number of experimental outcomes for the entire experiment can be calculated by multiplying the number of outcomes for each step together:

Number of outcomes for the first step: 3

Number of outcomes for the second step: 2

Number of outcomes for the third step: 4

Multiplying these numbers: 3 outcomes x 2 outcomes x 4 outcomes = 24 total experimental outcomes.

The population of City A was approximately 243000 people, and it increased by 8% in one year. What was the new population

Answers

Answer:

262,440

Step-by-step explanation:

Multiply the population (243000) times 8% (0.08)

   243000*0.08 = 19,440

Add the 8% to the total population

   19,440 + 243,000 = 262,440

The new population of City A after one year with an 8% of the increasing rate will be 262,440.

What is the percentage?

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

The number of inhabitants in City A was roughly 243000 individuals, and it expanded by 8% in one year.

The new population of City A after one year with an 8% of the increasing rate is given as,

⇒ (1 + 0.08) x 243,000

⇒ 1.08 x 243,000

⇒ 262,440

The new population of City A after one year with an 8% of the increasing rate will be 262,440.

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Need Help ASAP!!.

1. Error Analysis: Anita Help drew the triangle below. Her friend, Greta Life, told her that her triangle was incorrect. Who is correct? Explain.

2. The Geo Air pilot is looking at SCCA from the plane. From the aircraft the angle of depression is 17 degrees. If the plane is at an altitude of 10,000 feet, approximately how far is the plane to SCCA? Round your answer to the nearest tenth. The image is not drawn to scale.

3. Trey Rigg’s house is next to a large pine tree. The National Weather Center has issued a warning for high winds. Trey is worried that his house is at risk of being crushed by the pine tree. Trey’s house is 25 feet from the base of the tree and Trey calculates the angle of elevation to be 43 degrees from the base of his house. Find the height of the tree to determine if Trey’s house is at risk. Round your answer to the nearest tenth.

Picture 1 is for Number 1.
Picture 2 is for Number 2.
Picture 3 is for Number 3.

Answers

Answer:

Part 1) Greta's right, the triangle is incorrect.

Part 2) [tex]34,203\ ft[/tex]

Part 3) The height of the tree is [tex]23.3\ ft[/tex], Trey’s house is not at risk

Step-by-step explanation:

Part 1) we know that

In the right triangle of the figure

[tex]sin(30\°)=\frac{1}{2}[/tex]

[tex]sin(30\°)=\frac{6\sqrt{3}}{12}=\frac{\sqrt{3}}{2}[/tex]

Compare

[tex]\frac{1}{2}\neq\frac{\sqrt{3}}{2}[/tex]

therefore

The triangle is not correct

Because

The side adjacent to the 30 degree angle should be [tex]6\sqrt{3}[/tex] and the side opposite the 30 degree angle should be [tex]6[/tex]

Part 2)

Let

x--------> the distance from the airplane to the SCCA (hypotenuse of the right triangle)

we know that

[tex]sin(17\°)=\frac{10,000}{x}[/tex]

[tex]x=\frac{10,000}{sin(17\°)}[/tex]

[tex]x=34,203\ ft[/tex]

Part 3)

Let

x-------->  the height of the tree

we know that

[tex]tan(43\°)=\frac{h}{25}[/tex]

[tex]h=tan(43\°)(25)=23.3\ ft[/tex]

[tex]23.3\ ft< 25\ ft[/tex]

therefore

Trey’s house is not at risk

If A=[tex]\left[\begin{array}{ccc}-10&10&8\\-2&-1&5\\-4&8&-6\end{array}\right][/tex] and B= [tex]\left[\begin{array}{ccc}5&6&-4\\10&-6&-10\\-9&1&10\end{array}\right][/tex] , find -7A and -6B.

Answers

Answer:

Option c

Step-by-step explanation:

We have two matrices, matrix A and matrix B.

Before doing the addition of matrices, we must multiply the matrix A by the scalar -7 and then multiply the matrix B by the scalar -6.

The multiplication of a matrix A by a scalar c, is done by multiplying all the elements of matrix A by the value c.

So

[tex]-7A = \left[\begin{array}{ccc}70&-70&-56\\14&7&-35\\28&-56&42\end{array}\right]\\\\\\-6B =\left[\begin{array}{ccc}-30&-36&24\\-60&36&60\\54&-6&-60\end{array}\right][/tex]

Now we add both matrices.

The sum of the matrices is done by adding each term [tex]a_{mn}[/tex] with each term [tex]b_{mn}[/tex]

For example: (70 - 40) , (-70 + (-36)), ...,    

Then:

[tex]-7A + (-6B) = \left[\begin{array}{ccc}40&-106&-32\\-46&43&25\\82&-62&-18\end{array}\right][/tex]

The sum of four consecutive even integers is at least 244. Find the least possible value of the first integer.

Answers

x + x +1 + x +2 + x + 3 >= 244

=》 4x + 6 >= 244

=》 4x >= 238

=》 x >= 238/4 >= 59.5

since x is an integer...least value of x is 60

Answer:

The least possible even integer is 58

Step-by-step explanation:

Let's let x be an even integer. The next three would be shown by x+2, x+4 x+6 so now we can add all these to equal 244. Shown with an equation would look like:

x + x+2 + x+4 + x+6 = 244

Combine like terms will be:

4x+12=244

Subtract 12 from both sides we will get

4x=232

Now Divide each side by 4

x=58

So now put x in the above equation and we get  the numbers

x=58,

x+2= 60

X+4 =62

x+6= 64

The least one is 58

Julia bought 40 bags of compost each bag weighed 50 lb is how many tons of compost did she buy

Answers

Answer:

She bought .9 ton of compost.

Step-by-step explanation:

Take the amount of bags she bought and multiply it by the weight of each bag.

40*50=2,000

Then divide it by the amount a ton is.

2,000/2,204=0.90718474

Round it to the nearest tenth.

=.9

Then that's you're answer.

Complete the inequality statement.

14 ft ____ 4 1/2 yd.

Answers

Answer:

4.66667

Step-by-step explanation:

There are only a few roller coasters in the world whose path takes them underground. Suppose a portion of the roller coaster can be modeled by the function f(t) = (t^2 − 13t + 40)(t^2 − 2t + 3), where t represents the time elapsed in seconds since passing point A on the roller coaster and f(t) represents the height in feet above the ground.


Find the zeros of the function. What do these zeros represent in the context of the problem?



The thing is, I found the zeros ( which are [8,0] and [5,0]) but I don't know what they represent..

Answers

Answer: t=5 , t=8 on PLATO

Step-by-step explanation:

Final answer:

In the context of the problem, the zeros of the function represent the points in time when the roller coaster is at ground level. Specifically, the roller coaster goes underground at t = 5 seconds and comes back above ground at t = 8 seconds.

Explanation:

In the function f(t) = (t^2 − 13t + 40)(t^2 − 2t + 3), which models the height of the roller coaster above the ground, the zeros represent the points in time when the roller coaster is at ground level. In other words, when f(t) = 0, the height of the roller coaster is zero, implying it is at ground level. In your case, the zeros you found signify that the coaster is on the ground at the time instances t = 5 and t = 8 seconds since passing point A.

The values t = 5 and t = 8 seconds are the time instances when the roller coaster enters and exits the underground portion of the track respectively. It's crucial to comprehend the physical significance of mathematical solutions, particularly in real-world scenarios.

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